Question

Statement-l:
The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is ${}^9{C}_3$
Statement-2:
The number of ways of choosing any 3 places from 9 different places is ${}^9{C}_3$.

• A. Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
• B. Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
• C. Statement-1 is true, Statement-2 is false
• D. Statement-1 is false, Statement-2 is true.

Answer 1

The correct option is A Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

The number of ways of distributing $n$ identical objects among $r$ persons such that each person gets at least one object is same as the number of ways of selecting $(r-1)$ places out of $(n-1)$ different places, that is ${}^{n-1}{C}_{r-1}$.
${=}^{10-1}{C}_{4-1}$
${=}^9{C}_3$
Hence, option 'A' is correct.